2x^2=5x+21

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Solution for 2x^2=5x+21 equation:


Simplifying
2x2 = 5x + 21

Reorder the terms:
2x2 = 21 + 5x

Solving
2x2 = 21 + 5x

Solving for variable 'x'.

Reorder the terms:
-21 + -5x + 2x2 = 21 + 5x + -21 + -5x

Reorder the terms:
-21 + -5x + 2x2 = 21 + -21 + 5x + -5x

Combine like terms: 21 + -21 = 0
-21 + -5x + 2x2 = 0 + 5x + -5x
-21 + -5x + 2x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-21 + -5x + 2x2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-10.5 + -2.5x + x2 = 0

Move the constant term to the right:

Add '10.5' to each side of the equation.
-10.5 + -2.5x + 10.5 + x2 = 0 + 10.5

Reorder the terms:
-10.5 + 10.5 + -2.5x + x2 = 0 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + -2.5x + x2 = 0 + 10.5
-2.5x + x2 = 0 + 10.5

Combine like terms: 0 + 10.5 = 10.5
-2.5x + x2 = 10.5

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 10.5 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 10.5 + 1.5625

Combine like terms: 10.5 + 1.5625 = 12.0625
1.5625 + -2.5x + x2 = 12.0625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 12.0625

Calculate the square root of the right side: 3.473110997

Break this problem into two subproblems by setting 
(x + -1.25) equal to 3.473110997 and -3.473110997.

Subproblem 1

x + -1.25 = 3.473110997 Simplifying x + -1.25 = 3.473110997 Reorder the terms: -1.25 + x = 3.473110997 Solving -1.25 + x = 3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 3.473110997 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 3.473110997 + 1.25 x = 3.473110997 + 1.25 Combine like terms: 3.473110997 + 1.25 = 4.723110997 x = 4.723110997 Simplifying x = 4.723110997

Subproblem 2

x + -1.25 = -3.473110997 Simplifying x + -1.25 = -3.473110997 Reorder the terms: -1.25 + x = -3.473110997 Solving -1.25 + x = -3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -3.473110997 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -3.473110997 + 1.25 x = -3.473110997 + 1.25 Combine like terms: -3.473110997 + 1.25 = -2.223110997 x = -2.223110997 Simplifying x = -2.223110997

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.723110997, -2.223110997}

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